How to get probabilities from a simulator without sampling for a Qiskit circuit with measurement throughout

Question

Suppose we have a Qiskit circuit like

from qiskit import QuantumCircuit

qc = QuantumCircuit(1,1)
qc.h(0)
qc.measure(0,0)

If we want to find the probabilities for each outcome (by simulation) the usual method is to run it for many shots.

from qiskit import Aer

backend = Aer.get_backend('aer_simulator')

shots = 1024
counts = backend.run(qc,shots=shots).result().get_counts()

This will tell us how many shots came out for each result, and then we can estimate the probabilities from this.

probs = {string:count/shots for string,count in counts.items()}

However, since all measurements are at the end in this case, we can actually get the exact probabilities without sampling. Just replace the measurement with save_state() and extract the result from the data attribute of result.

qc = QuantumCircuit(1,1)
qc.h(0)
qc.save_state()

probs = backend.run(qc,shots=1).result().data()['stabilizer'].probabilities_dict()

Is it possible to do something similar for a circuit with measurements throughout, such as the following?

from qiskit import QuantumCircuit

qc = QuantumCircuit(1,2)
qc.h(0)
qc.measure(0,0)
qc.h(0)
qc.measure(0,1)

Putting save_state after measurements seems to produce an output for given shots. So a naive adaption of the same process doesn't work without sampling.

Answer 1

As I have understood, what you are asking for is to see the probability outcome of state in different places of a circuit without actually performing a measurement in those places. The following code using qiskit.quantum_info.Statevector.probabilities can be helpful.

For more details on qiskit.quantum_info.Statevector you can look here.

Answer 2

Create your own QuantumCircuit without measurement gates and classical bits,

from qiskit import QuantumRegister, QuantumCircuit, Aer
from qiskit.quantum_info import Statevector
import numpy as np

q = QuantumRegister(1)

qc = QuantumCircuit(q)

qc.u(np.pi/4,np.pi/4,np.pi/4, q)

qc.draw()

    ┌────────────────┐
q0: ┤ U(π/4,π/4,π/4) ├
    └────────────────┘

and then measure probabilities:

backend = Aer.get_backend('statevector_simulator')

outputstate = backend.run(qc, shots=1).result().get_statevector()

probs = Statevector(outputstate).probabilities()

print(probs)

[0.85355339 0.14644661]